Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 3x - 7$ and $ KL = 5x - 19$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {3x - 7} = {5x - 19}$ Solve for $x$ $ -2x = -12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 3({6}) - 7$ $ KL = 5({6}) - 19$ $ JK = 18 - 7$ $ KL = 30 - 19$ $ JK = 11$ $ KL = 11$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {11} + {11}$ $ JL = 22$